Simplicial presheaf

Okay, imagine you are building with blocks. You can choose different shapes of blocks like cubes, pyramids, etc. to build something cool. Now, instead of just using blocks, let's add some rules. We can only connect blocks in certain ways to create specific shapes.

A simplicial presheaf is kind of like building with blocks that follow certain rules. Except, the blocks are replaced with sets of objects and the rules are replaced with functions that tell us how to connect them to create certain shapes.

Let's say we have a simplicial presheaf on a space, which is just a fancy way of saying we have a collection of sets of objects that we want to connect in a certain way. We can think of each set as being a block and the functions as being the rules for how to connect the sets.

One important thing to remember is that these sets have something called "dimension". In blocks, the dimension could be the number of sides or faces they have. In simplicial presheaf, dimension is measured by how many sets are connected to each other in a straight line.

So, a simplicial presheaf is like building with sets of objects that follow rules for how they can be connected, and the dimension is based on how many sets are connected in a straight line.